<p>The value of \(\dfrac{dy}{dx}\) for the curve \(2y = 3 - x^2\) is</p>
Step-by-Step Solution
Key Concept: Implicitly differentiate both sides of the equation with respect to x, treating y as a function of x. The derivative of a constant is 0, and apply the power rule to polynomial terms.
<p><strong>Step 1:</strong> Start with the equation: 2y = 3 - x²</p><p><strong>Step 2:</strong> Differentiate both sides with respect to x:</p><p>d/dx(2y) = d/dx(3 - x²)</p><p><strong>Step 3:</strong> Apply differentiation rules:</p><p>2(dy/dx) = 0 - 2x</p><p><strong>Step 4:</strong> Solve for dy/dx:</p><p>2(dy/dx) = -2x</p><p>dy/dx = -x</p><p>∴ Answer: B (dy/dx = -x)</p>
Correct Answer: B